Coggle

Like everyone else on vacation, the cows play the cow version of the word game Boggle, called Coggle. In this game, 25 letter dice are rolled into a $5 \times 5$ matrix like this one:

Z C C D X
K Q M N B
U O W Z Y
F C O I J
P A Q Z T

A word is made by starting at some letter and repeatedly moving to one of its (up to) eight neighbors, until the successive letters spell out a word from the dictionary. Cells that touch horizontally, vertically, or diagonally are neighbors. A word may not use the letter of the same die twice.

In the matrix above, the lower 'C' can be used to form the words "CAP", "COW", and "COOK", but not "COD" or "PACK". With the dictionary of the original problem, the complete list of words that can be formed in the matrix above is "CAP", "COOK", "COW", "OWN", "WIT", "WOO", "ZOO", and "ZOOM".

Help Bessie see how well she can do. Given five rows of five letters that represent the dice, and a dictionary, count how many words from the dictionary can be formed.

A word might be formed in more than one way. Such a word is still counted only once.

Lines 1 to 5 describe the matrix. Line $i$ contains five space-separated uppercase letters that form row $i$.

Line 6 contains $N$, the number of words in the dictionary ($1 \le N < 25\,000$).

Each of the next $N$ lines contains one dictionary word. Every word is a string of $1$ to $20$ uppercase letters, and all words are distinct.

Print a single integer: the number of dictionary words that can be formed using the rules above.